Student Question

# Bayleaf Inc is considering the purchase of a machine that costs \$250,000. The machine is expected to generate revenues of \$85,000 per year for five years. The machine would be depreciated using the straight-line method over a five-year life and have no salvage value. The company considers the impact of income taxes in all of its capital investment decisions. The company has a 40 percent income tax rate and desires an after-tax rate of return of 12 percent on its investmentCompute the net present value of the machine.

Two main equations are required to solve this problem, the first has to do with depreciation rate, and the second with after-tax revenue.

As to the first, if a \$250,000 investment has no salvage value after 5 years, it's depreciate rate is \$50,000/year. We use this alongside the annual revenue to calculate general income before tax, as follows: \$85,000-\$50,000=\$35,000.

Taxable revenue=before tax revenue * (tax rate).

Thus, taxable revenue = \$35,000 * (.4) =\$14,000.

So, each year will have an annual net revenue of \$85,000-\$14,000 = \$71,000

We now use those figures to compute the present value:

future value = \$71,000+\$71,000*1.12+\$71,000*1.12^2+\$71,000*1.12^3+\$71,000*1.12^4 = \$451,000

present value = future value/(1+r)^n, where r is the interest rate, and n is the number of years. Thus, the present value is \$451,000/(1.12)^5 = \$255,909

Net present value = present value - cost = \$255,909-\$250,000 = \$5,909